English

Find the general solution of the differential equation dydxdydx=yx. - Mathematics

Advertisements
Advertisements

Question

Find the general solution of the differential equation `"dy"/"dx" = y/x`.

Sum

Solution

`"dy"/"dx" = y/x`

⇒ `"dy"/y = "dx"/x`

⇒ `int "dy"/y = int "dx"/x`

⇒ logy = logx + logc

⇒ y = cx

shaalaa.com
  Is there an error in this question or solution?
Chapter 9: Differential Equations - Solved Examples [Page 181]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 12
Chapter 9 Differential Equations
Solved Examples | Q 2 | Page 181

RELATED QUESTIONS

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.

`x/a + y/b = 1`


Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.

y2 = a (b2 – x2)


Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.

y = a e3x + b e– 2x


Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.

y = e2x (a + bx)


Find a particular solution of the differential equation (x - y) (dx + dy) = dx - dy, given that y = -1, when x = 0. (Hint: put x - y = t)


The general solution of the differential equation `(y dx - x dy)/y = 0` is ______.


The general solution of a differential equation of the type  `dx/dy + P_1 x = Q_1` is ______.


Show that y2 − x2 − xy = a is a solution of the differential equation \[\left( x - 2y \right)\frac{dy}{dx} + 2x + y = 0.\]


Verify that y = A cos x + sin x satisfies the differential equation \[\cos x\frac{dy}{dx} + \left( \sin x \right)y=1.\]


\[\frac{dy}{dx} = \sin^3 x \cos^4 x + x\sqrt{x + 1}\]


\[\frac{dy}{dx} = y^2 + 2y + 2\]


\[\frac{dy}{dx} = x^2 e^x\]


\[\frac{dy}{dx} = \sin^3 x \cos^2 x + x e^x\]


tan y dx + tan x dy = 0


cosec x (log y) dy + x2y dx = 0


(1 − x2) dy + xy dx = xy2 dx


A solution of the differential equation `("dy"/"dx")^2 - x "dy"/"dx" + y` = 0 is ______.


Solve the differential equation:

cosec3 x dy − cosec y dx = 0


The general solution of the differential equation `(dy)/(dx) + x/y` = 0 is


If n is any integer, then the general solution of the equation `cos x - sin x = 1/sqrt(2)` is


General solution of tan 5θ = cot 2θ is


The general solution of the differential equation `(dy)/(dx) = e^(x + y)` is


The general solution of the differential equation `(ydx - xdy)/y` = 0


Find the general solution of differential equation `(dy)/(dx) = (1 - cosx)/(1 + cosx)`


What is the general solution of differential equation `(dy)/(dx) = sqrt(4 - y^2)  (-2 < y < 2)`


The general solution of the differential equation ydx – xdy = 0; (Given x, y > 0), is of the form

(Where 'c' is an arbitrary positive constant of integration)


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×